i'd add her on the 10k card, it might take a few months before she will be able to get her own card though, and make sure you add her you make sure they put in her social security number, sometimes they only ask the name.
As she is/will be a student, she should be eligible for student cards at some point. I think adding her as an AU is the way to go, then at 6 months or a year, apply for some of the student cards.
That of course is just based on my experience, we didn't have secured cards. I had added my daughters as AUs on my Cap One card (and one also on the BCP).
In her first year in college, my younger daughter has two cards of her own (Cap One Journey and Citi Forward for Students) and the elder, graduating this year, has those plus a BCE.
Starting my rebuild!